🧠 GWAS Fundamentals

Q: What is GWAS?

GWAS (Genome-Wide Association Study) is a method to identify genetic variants (usually SNPs) associated with a trait or disease. It tests millions of SNPs across the genome for statistical association with a phenotype, using large cohorts of individuals.

Q: What is a SNP?

A SNP (Single Nucleotide Polymorphism) is a variation at a single position in DNA where different individuals have different nucleotides (e.g., A, T, C, or G). SNPs are the most common genetic variants and are the primary markers used in GWAS.

Q: What is population structure and why does it matter in GWAS?

Population structure refers to systematic differences in allele frequencies between subpopulations. It matters in GWAS because it can cause spurious associations (false positives) if cases and controls have different ancestry. Methods like PCA, ADMIXTURE, and linear mixed models correct for structure.

Q: What is linkage disequilibrium (LD)?

Linkage disequilibrium (LD) is the non-random association of alleles at different loci. High LD means alleles are inherited together more often than expected by chance. LD is used to identify haplotype blocks and to perform imputation and fine-mapping in GWAS.

Q: Which tools are used for GWAS?

Common GWAS tools include PLINK (association testing, QC), GCTA (mixed models, heritability), BOLT-LMM (large-scale LMM), GEMMA (mixed models), SAIGE (binary traits, related individuals), and REGENIE (whole-genome regression). Visualization is done with QQ plots and Manhattan plots.

🎯 What is GWAS?

GWAS (Genome-Wide Association Study) is a method to identify genetic variants (usually SNPs) associated with a trait or disease. It tests millions of SNPs across the genome for statistical association with a phenotype, using large cohorts of individuals. GWAS has revolutionized our understanding of the genetic basis of complex traits and diseases, from height and BMI to diabetes and schizophrenia.

Why GWAS Matters

Discovery: Find risk variants. Biology: Understand mechanisms. Prediction: Polygenic scores. Drugs: Target identification. Personalized: Precision medicine. Populations: Evolutionary insights.

📌 SNP📌 Association📌 Structure📌 LD

# GWAS & Population Genetics — the big picture
# Finding genetic variants associated with traits.

print("""
=== GWAS & Population Genetics ===

What it is:
  - Genome-wide association study
  - Millions of SNPs
  - Trait / disease
  - Statistical association

Why it matters:
  - Discover risk variants
  - Understand biology
  - Polygenic scores
  - Drug targets
  - Precision medicine
  - Evolutionary insights

Key concepts:
  - SNP (single nucleotide polymorphism)
  - Linkage disequilibrium (LD)
  - Hardy-Weinberg equilibrium (HWE)
  - Population structure
  - Association testing
  - Mixed models
  - Manhattan plot
  - QQ plot
  - Fine-mapping
  - Imputation

Applications:
  - Disease genetics
  - Complex traits
  - Agriculture
  - Evolutionary biology
  - Pharmacogenomics
  - Personalized medicine
""")

print("=== Historical Context ===")
print("""
2005: First GWAS (age-related macular degeneration)
2007: Wellcome Trust Case Control Consortium
2010: Thousands of GWAS
2015: Biobanks (UK Biobank)
2020: Millions of individuals
2025: Multi-omics, diverse populations, PRS
""")

print("=== Why It's Hard ===")
print("""
1. MULTIPLE TESTING
   - Millions of SNPs
   - Bonferroni: 5e-8
   - False positives

2. POPULATION STRUCTURE
   - Ancestry differences
   - Spurious associations
   - Correction needed

3. LINKAGE DISEQUILIBRIUM
   - Correlated SNPs
   - Fine-mapping hard
   - Causal variants

4. EFFECT SIZE
   - Small effects
   - Large samples needed
   - Missing heritability

5. RARE VARIANTS
   - Not on arrays
   - Sequencing needed
   - Statistical power
""")

🎯 Why GWAS Matters

🎯 The Value of GWAS

GWAS has identified thousands of genetic variants associated with hundreds of traits and diseases, transforming our understanding of complex genetics.

Key Benefits

Discovery: Risk variants. Biology: Mechanisms. Prediction: PRS. Drugs: Targets. Precision: Medicine. Evolution: Selection.

🎯 Discovery🎯 Biology🎯 Prediction🎯 Drugs

# Why GWAS Matters
print("=== 1. Discovery of Risk Variants ===")
print("""
Discovery:
  - Thousands of associations
  - Many traits
  - Many diseases

Example:
  Height: ~10,000 SNPs
  BMI: ~1,000 SNPs
  Schizophrenia: ~300 loci
  Diabetes: ~400 loci
""")

print("\n=== 2. Understanding Biology ===")
print("""
Biology:
  - Mechanisms
  - Pathways
  - Drug targets

Example:
  PCSK9 → cholesterol
  → Drug (evolocumab)
  → Approved
""")

print("\n=== 3. Polygenic Scores ===")
print("""
PRS:
  - Polygenic risk score
  - Sum of effect sizes
  - Prediction

Example:
  Height PRS
  → Predict height
  → ~80% accuracy
""")

print("\n=== 4. Drug Discovery ===")
print("""
Drug:
  - Target identification
  - Validation
  - Repurposing

Example:
  GWAS → target
  → Drug
  → Clinical trial
""")

print("\n=== 5. Precision Medicine ===")
print("""
Precision:
  - Personalized risk
  - Treatment
  - Prevention

Example:
  Breast cancer
  → BRCA1/2
  → Screening
""")

print("\n=== 6. Evolutionary Insights ===")
print("""
Evolution:
  - Selection
  - Adaptation
  - Migration

Example:
  Lactase persistence
  → Selection
  → Europeans
""")

print("\n=== 7. Agriculture ===")
print("""
Agriculture:
  - Crop traits
  - Breeding
  - Food security

Example:
  Rice yield
  → GWAS
  → Breeding
""")

print("\n=== 8. Pharmacogenomics ===")
print("""
Pharmacogenomics:
  - Drug response
  - Adverse effects
  - Dosing

Example:
  CYP2C19
  → Clopidogrel
  → Dosing
""")

print("\n=== 9. Missing Heritability ===")
print("""
Missing heritability:
  - GWAS explains some
  - Rare variants
  - Epistasis
  - Epigenetics

Example:
  Height: ~80% heritable
  GWAS: ~50% explained
  Missing: ~30%
""")

print("\n=== 10. Multi-Omics ===")
print("""
Multi-omics:
  - GWAS + transcriptomics
  - GWAS + proteomics
  - GWAS + metabolomics

Example:
  eQTL
  → Gene expression
  → Mechanism
""")

🔬 SNPs & Genotyping

🎯 Single Nucleotide Polymorphisms

SNPs (Single Nucleotide Polymorphisms) are the most common genetic variants, occurring at ~1 in 1,000 bases. They are the primary markers used in GWAS.

SNPs

Definition: Single base change. Frequency: >1%. Genotyping: Arrays. Imputation: Fill missing. MAF: Minor allele. HWE: Equilibrium.

🔬 SNP🔬 MAF🔬 Genotyping🔬 Imputation

# SNPs & Genotyping
print("=== What is a SNP? ===")
print("""
SNP:
  - Single base change
  - A → T, C → G, etc.
  - > 1% frequency
  - Most common variant

Example:
  Individual 1: ...ACGT...
  Individual 2: ...ATGT...
  → SNP at position 2 (C/T)
""")

print("\n=== SNP Types ===")
print("""
Types:
  - Transition: A↔G, C↔T
  - Transversion: A↔C, A↔T, G↔C, G↔T
  - Synonymous: no amino acid change
  - Non-synonymous: amino acid change

Example:
  rs123456
  → A/G
""")

print("\n=== Genotyping ===")
print("""
Genotyping:
  - Microarray
  - Sequencing
  - TaqMan
  - MassArray

Arrays:
  - Illumina
  - Affymetrix
  - ~500K-2M SNPs

Example:
  Illumina Global Screening Array
  → 700K SNPs
""")

print("\n=== Genotype Calls ===")
print("""
Genotype:
  - 0/0: homozygous reference
  - 0/1: heterozygous
  - 1/1: homozygous alternate

Example:
  rs123456
  Individual 1: 0/0 (AA)
  Individual 2: 0/1 (AG)
  Individual 3: 1/1 (GG)
""")

print("\n=== MAF ===")
print("""
MAF:
  - Minor allele frequency
  - Frequency of minor allele
  - 0 to 0.5

Example:
  Allele A: 70%
  Allele G: 30%
  MAF = 0.3
""")

print("\n=== HWE ===")
print("""
HWE:
  - Hardy-Weinberg equilibrium
  - Expected genotype frequencies
  - p² + 2pq + q² = 1

Example:
  p = 0.7 (A)
  q = 0.3 (G)
  AA: 0.49
  AG: 0.42
  GG: 0.09
""")

print("\n=== QC ===")
print("""
QC:
  - Call rate
  - MAF
  - HWE
  - Heterozygosity
  - Relatedness

Example:
  Call rate > 95%
  MAF > 1%
  HWE p > 1e-6
""")

print("\n=== Imputation ===")
print("""
Imputation:
  - Fill missing genotypes
  - Reference panel
  - Increases SNPs

Example:
  Array: 700K SNPs
  Imputed: 10M SNPs
""")

print("\n=== Python Genotype ===")
print("""
import numpy as np

def genotype_stats(genotypes):
    \"\"\"Compute genotype statistics.\"\"\"
    n = len(genotypes)
    ref = genotypes.count(0) + genotypes.count('0/0')
    het = genotypes.count(1) + genotypes.count('0/1')
    alt = genotypes.count(2) + genotypes.count('1/1')
    
    maf = (2 * alt + het) / (2 * n)
    
    return {
        'ref': ref,
        'het': het,
        'alt': alt,
        'maf': maf
    }

# Example
genotypes = [0, 0, 1, 1, 2, 1, 0, 1]
stats = genotype_stats(genotypes)
print(stats)
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - GWAS
  - Population genetics
  - Forensics
  - Ancestry
  - Pharmacogenomics
  - Breeding
""")

🔗 Linkage Disequilibrium

🎯 Non-Random Association

Linkage disequilibrium (LD) is the non-random association of alleles at different loci. High LD means alleles are inherited together more often than expected by chance.

LD

Definition: Non-random. D: Disequilibrium. D': Normalized. r²: Correlation. Blocks: Haplotypes. Fine-mapping: Use LD.

🔗 D🔗 D'🔗 r²🔗 Blocks

# Linkage Disequilibrium
print("=== What is LD? ===")
print("""
LD:
  - Non-random association
  - Alleles at different loci
  - Inherited together
  - More than expected

Example:
  Locus A: A/G
  Locus B: C/T
  
  If A always with C:
  → LD
""")

print("\n=== Measures ===")
print("""
D:
  - Disequilibrium coefficient
  - D = P(AB) - P(A)P(B)
  - Range: -0.25 to 0.25

D':
  - Normalized D
  - Range: 0 to 1
  - D' = 1: complete LD

r²:
  - Correlation
  - Range: 0 to 1
  - r² = 1: perfect LD
  - Most common
""")

print("\n=== LD Example ===")
print("""
Example:
  Locus A: A (p=0.7), G (q=0.3)
  Locus B: C (p=0.6), T (q=0.4)
  
  Observed:
    AC: 0.5
    AT: 0.2
    GC: 0.1
    GT: 0.2
  
  Expected (no LD):
    AC: 0.7*0.6 = 0.42
    AT: 0.7*0.4 = 0.28
    GC: 0.3*0.6 = 0.18
    GT: 0.3*0.4 = 0.12
  
  D = 0.5 - 0.42 = 0.08
  → LD
""")

print("\n=== LD Blocks ===")
print("""
LD blocks:
  - Regions of high LD
  - Haplotype blocks
  - Fewer tag SNPs

Example:
  Block 1: SNPs 1-10
  Block 2: SNPs 11-20
  Block 3: SNPs 21-30
""")

print("\n=== Tag SNPs ===")
print("""
Tag SNPs:
  - Representative SNPs
  - Capture LD
  - Reduce genotyping

Example:
  Block with 10 SNPs
  → 2 tag SNPs
  → Capture all
""")

print("\n=== LD and GWAS ===")
print("""
LD in GWAS:
  - Association signal
  - Tag SNP
  - Causal variant

Example:
  Causal variant not genotyped
  → Tag SNP in LD
  → Association
""")

print("\n=== LD and Fine-Mapping ===")
print("""
Fine-mapping:
  - Identify causal variant
  - LD structure
  - Credible set

Example:
  Association at rs123
  → LD with rs456
  → Causal?
""")

print("\n=== LD Calculation ===")
print("""
r²:
  r² = D² / (p_A * q_A * p_B * q_B)

Example:
  D = 0.08
  p_A = 0.7, q_A = 0.3
  p_B = 0.6, q_B = 0.4
  
  r² = 0.08² / (0.7 * 0.3 * 0.6 * 0.4)
     = 0.0064 / 0.0504
     = 0.127
""")

print("\n=== Python LD ===")
print("""
import numpy as np

def ld_r2(geno_a, geno_b):
    \"\"\"Compute r² between two SNPs.\"\"\"
    a = np.array(geno_a)
    b = np.array(geno_b)
    
    # Allele frequencies
    p_a = a.mean() / 2
    p_b = b.mean() / 2
    
    # D
    d = np.mean((a - 2*p_a) * (b - 2*p_b)) / 2
    
    # r²
    r2 = d**2 / (p_a * (1-p_a) * p_b * (1-p_b))
    return r2

# Example
a = [0, 0, 1, 1, 2, 1, 0, 1]
b = [0, 1, 1, 0, 2, 1, 0, 0]
print(f"r² = {ld_r2(a, b):.3f}")
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - GWAS
  - Fine-mapping
  - Imputation
  - Tag SNPs
  - Haplotypes
  - Selection
""")

⚖️ Hardy-Weinberg Equilibrium

🎯 HWE

Hardy-Weinberg Equilibrium (HWE) states that allele and genotype frequencies in a population remain constant from generation to generation in the absence of evolutionary forces.

HWE

Equation: p² + 2pq + q² = 1. p: Allele 1. q: Allele 2. Equilibrium: No evolution. Deviation: QC. Test: Chi-square.

⚖️ p² + 2pq + q²⚖️ Chi-square⚖️ QC⚖️ Deviation

# Hardy-Weinberg Equilibrium
print("=== HWE Equation ===")
print("""
HWE:
  - p² + 2pq + q² = 1
  - p: frequency of allele A
  - q: frequency of allele a
  - p + q = 1

Genotypes:
  AA: p²
  Aa: 2pq
  aa: q²
""")

print("\n=== Example ===")
print("""
Example:
  p = 0.7 (A)
  q = 0.3 (a)

  AA: 0.7² = 0.49
  Aa: 2*0.7*0.3 = 0.42
  aa: 0.3² = 0.09
  
  Total: 1.00
""")

print("\n=== HWE Test ===")
print("""
Test:
  - Chi-square
  - Observed vs expected
  - p-value

Example:
  Observed:
    AA: 50
    Aa: 40
    aa: 10
  
  Expected (p=0.7):
    AA: 49
    Aa: 42
    aa: 9
  
  Chi-square = 0.20
  p = 0.90
  → HWE
""")

print("\n=== HWE in GWAS ===")
print("""
HWE in GWAS:
  - QC filter
  - p > 1e-6
  - Remove deviant SNPs

Reasons for deviation:
  - Genotyping error
  - Population structure
  - Selection
  - Copy number
""")

print("\n=== HWE Python ===")
print("""
from scipy.stats import chisquare
import numpy as np

def hwe_test(obs_aa, obs_ab, obs_bb):
    \"\"\"Test HWE.\"\"\"
    n = obs_aa + obs_ab + obs_bb
    p = (2 * obs_aa + obs_ab) / (2 * n)
    q = 1 - p
    
    exp_aa = p**2 * n
    exp_ab = 2 * p * q * n
    exp_bb = q**2 * n
    
    chi2, pval = chisquare([obs_aa, obs_ab, obs_bb],
                           [exp_aa, exp_ab, exp_bb])
    return chi2, pval

# Example
chi2, p = hwe_test(50, 40, 10)
print(f"Chi2: {chi2:.3f}, p: {p:.3f}")
""")

print("\n=== Deviation ===")
print("""
Deviation:
  - Excess heterozygotes
  - Deficiency
  - Reasons

Excess het:
  - Genotyping error
  - Population structure

Deficiency:
  - Inbreeding
  - Selection
  - Null alleles
""")

print("\n=== QC Filter ===")
print("""
Filter:
  - HWE p > 1e-6
  - Remove deviant
  - Per SNP

Example:
  PLINK:
  --hwe 1e-6
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - QC
  - Population genetics
  - Selection
  - Genotyping error
  - Association
""")

🗺️ Population Structure

🎯 Population Structure

Population structure refers to systematic differences in allele frequencies between subpopulations. It can cause spurious associations in GWAS if not corrected.

Structure

PCA: Principal components. ADMIXTURE: Ancestry. LMM: Mixed models. Correction: Essential. Spurious: False positives. Ancestry: Differences.

🗺️ PCA🗺️ ADMIXTURE🗺️ LMM🗺️ Correction

# Population Structure
print("=== What is Population Structure? ===")
print("""
Structure:
  - Allele frequency differences
  - Subpopulations
  - Ancestry

Example:
  European: A allele 70%
  African: A allele 30%
  Asian: A allele 50%
""")

print("\n=== PCA ===")
print("""
PCA:
  - Principal Component Analysis
  - Dimensionality reduction
  - Population structure

Example:
  PC1: African vs European
  PC2: Asian vs European
  PC3: ...
""")

print("\n=== ADMIXTURE ===")
print("""
ADMIXTURE:
  - Ancestry estimation
  - Admixture proportions
  - K populations

Example:
  Individual 1: 80% EUR, 20% AFR
  Individual 2: 50% EUR, 50% AFR
""")

print("\n=== Correction Methods ===")
print("""
Methods:
  1. PCA correction
     - Include PCs as covariates
     
  2. Linear mixed models (LMM)
     - Random effect
     - Kinship matrix
     
  3. Genomic control
     - Inflation factor
     
  4. Structured association
     - ADMIXTURE
""")

print("\n=== PCA in PLINK ===")
print("""
PLINK:
  --pca 10
  → 10 PCs

Example:
  plink --bfile data --pca 10 --out pca
  → pca.eigenvec
  → pca.eigenval
""")

print("\n=== LMM ===")
print("""
LMM:
  - Linear mixed model
  - Fixed effects: SNPs, covariates
  - Random effects: kinship
  - Corrects structure

Example:
  y = Xβ + Zu + e
  u ~ N(0, σ²K)
  e ~ N(0, σ²I)
""")

print("\n=== Kinship Matrix ===")
print("""
Kinship:
  - Relatedness matrix
  - Genetic similarity
  - Random effect

Example:
  K = (1/n) * Σ (G_i - 2p_i)(G_i - 2p_i)^T
""")

print("\n=== Genomic Control ===")
print("""
GC:
  - Inflation factor λ
  - λ = median(χ²) / 0.456
  - Correct p-values

Example:
  λ = 1.0: no inflation
  λ = 1.1: mild inflation
  λ = 1.5: severe inflation
""")

print("\n=== Python PCA ===")
print("""
import numpy as np
from sklearn.decomposition import PCA

def population_pca(genotypes):
    \"\"\"PCA on genotypes.\"\"\"
    pca = PCA(n_components=10)
    pcs = pca.fit_transform(genotypes)
    return pcs, pca.explained_variance_ratio_

# Example
# genotypes = load_genotypes()
# pcs, var = population_pca(genotypes)
# print(f"PC1: {var[0]:.2%}")
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - GWAS correction
  - Ancestry inference
  - Admixture mapping
  - Population genetics
  - Evolutionary studies
""")

📊 Association Testing

🎯 Testing SNP-Trait Associations

Association testing tests each SNP for statistical association with a trait. It's the core of GWAS.

Association

Linear: Quantitative. Logistic: Binary. Covariates: Age, sex, PCs. Test: t-test, chi-square. Threshold: 5e-8. Effect: Beta, OR.

📊 Linear📊 Logistic📊 Covariates📊 Threshold

# Association Testing
print("=== Types of Traits ===")
print("""
Quantitative:
  - Height, BMI, blood pressure
  - Linear regression

Binary:
  - Disease (case/control)
  - Logistic regression
""")

print("\n=== Linear Regression ===")
print("""
Linear:
  y = μ + β*SNP + covariates + e

Test:
  - H0: β = 0
  - H1: β ≠ 0
  - t-test
  - p-value

Example:
  y = height
  SNP = 0, 1, 2
  β = effect size
""")

print("\n=== Logistic Regression ===")
print("""
Logistic:
  logit(P(y=1)) = μ + β*SNP + covariates

Test:
  - H0: β = 0
  - H1: β ≠ 0
  - Wald test
  - p-value

Example:
  y = disease (0/1)
  SNP = 0, 1, 2
  OR = exp(β)
""")

print("\n=== Covariates ===")
print("""
Covariates:
  - Age
  - Sex
  - PCs (population structure)
  - Batch
  - BMI

Example:
  y ~ SNP + age + sex + PC1 + PC2 + ...
""")

print("\n=== Multiple Testing ===")
print("""
Multiple testing:
  - Millions of SNPs
  - Bonferroni: 0.05 / 1M = 5e-8
  - FDR

Threshold:
  - Genome-wide: 5e-8
  - Suggestive: 1e-5

Example:
  p < 5e-8: significant
  p < 1e-5: suggestive
""")

print("\n=== PLINK Association ===")
print("""
PLINK:
  --linear (quantitative)
  --logistic (binary)

Example:
  plink --bfile data --linear --pheno pheno.txt --covar covar.txt --out assoc
  plink --bfile data --logistic --pheno pheno.txt --covar covar.txt --out assoc
""")

print("\n=== Output ===")
print("""
Output:
  CHR: chromosome
  SNP: SNP ID
  BP: position
  A1: effect allele
  TEST: test
  NMISS: samples
  BETA: effect size
  STAT: statistic
  P: p-value
  OR: odds ratio (logistic)

Example:
  1  rs123  100  A  ADD  1000  0.05  3.2  0.001
""")

print("\n=== Python Association ===")
print("""
import numpy as np
from scipy import stats
import statsmodels.api as sm

def association_test(genotype, phenotype, covariates=None):
    \"\"\"Test SNP-phenotype association.\"\"\"
    # Design matrix
    X = genotype.reshape(-1, 1)
    if covariates is not None:
        X = np.hstack([X, covariates])
    X = sm.add_constant(X)
    
    # Linear regression
    model = sm.OLS(phenotype, X).fit()
    beta = model.params[1]
    pval = model.pvalues[1]
    
    return beta, pval

# Example
# genotype = np.array([0, 0, 1, 1, 2, 1, 0, 1])
# phenotype = np.array([1.2, 1.5, 1.8, 1.9, 2.1, 1.7, 1.3, 1.6])
# beta, pval = association_test(genotype, phenotype)
# print(f"Beta: {beta:.3f}, p: {pval:.3e}")
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - GWAS
  - Candidate gene
  - QTL mapping
  - PheWAS
  - Rare variant
""")

🧮 Mixed Models (LMM)

🎯 Linear Mixed Models

Linear mixed models (LMM) account for population structure and relatedness by including a random effect based on a kinship matrix. They are the gold standard for GWAS.

LMM

Fixed: SNPs, covariates. Random: Kinship. Corrects: Structure. Power: High. Tools: GCTA, BOLT-LMM, GEMMA. Standard: GWAS.

🧮 Fixed🧮 Random🧮 Kinship🧮 Corrects

# Mixed Models
print("=== LMM Equation ===")
print("""
y = Xβ + Zu + e

y: phenotype
X: fixed effects (SNP, covariates)
β: fixed effects
Z: random effects design
u: random effects (kinship)
e: residuals

u ~ N(0, σ²_g K)
e ~ N(0, σ²_e I)
""")

print("\n=== Kinship Matrix ===")
print("""
Kinship:
  - Relatedness
  - Genetic similarity
  - Random effect

K = (1/n) * Σ (G_i - 2p_i)(G_i - 2p_i)^T

Example:
  K[i,j] = relatedness between i and j
""")

print("\n=== Variance Components ===")
print("""
Variance:
  - σ²_g: genetic variance
  - σ²_e: environmental variance
  - h² = σ²_g / (σ²_g + σ²_e)

Example:
  h² = 0.5
  → 50% heritability
""")

print("\n=== Tools ===")
print("""
1. GCTA
   - Mixed model
   - Heritability
   - Fast

2. BOLT-LMM
   - Large-scale
   - Fast
   - UK Biobank

3. GEMMA
   - Mixed model
   - Multiple phenotypes
   - Bayesian

4. SAIGE
   - Binary traits
   - Related individuals
   - Scalable

5. REGENIE
   - Whole-genome regression
   - Fast
   - Large-scale
""")

print("\n=== GCTA ===")
print("""
GCTA:
  - Genome-wide Complex Trait Analysis
  - Heritability
  - Mixed model

Commands:
  gcta --bfile data --make-grm --out grm
  gcta --grm grm --pheno pheno.txt --reml --out h2
  gcta --grm grm --mlma --bfile data --out assoc
""")

print("\n=== BOLT-LMM ===")
print("""
BOLT-LMM:
  - Large-scale
  - Fast
  - UK Biobank

Command:
  bolt --bfile=data --phenoFile=pheno.txt --lmm --LDscoresFile=LD.txt
""")

print("\n=== GEMMA ===")
print("""
GEMMA:
  - Mixed model
  - Multiple phenotypes

Commands:
  gemma -bfile data -gk 1 -o kinship
  gemma -bfile data -k kinship.cXX.txt -lmm 1 -o assoc
""")

print("\n=== SAIGE ===")
print("""
SAIGE:
  - Binary traits
  - Related individuals
  - Scalable

Command:
  saige --bfile=data --phenoFile=pheno.txt --phenoCol=disease
""")

print("\n=== REGENIE ===")
print("""
REGENIE:
  - Whole-genome regression
  - Fast
  - Large-scale

Commands:
  regenie --step 1 --bfile data --phenoFile pheno.txt
  regenie --step 2 --bfile data --phenoFile pheno.txt --pred pred.list
""")

print("\n=== Heritability ===")
print("""
Heritability:
  - SNP heritability
  - h²_SNP
  - Variance explained

Example:
  h² = 0.5
  → 50% variance explained
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - GWAS
  - Heritability
  - Prediction
  - Related individuals
  - Biobanks
""")

📈 Manhattan & QQ Plots

🎯 Visualizing GWAS Results

Manhattan plots and QQ plots are the standard visualizations for GWAS results. They reveal significant associations and assess model quality.

Plots

Manhattan: Genome-wide. QQ: p-value distribution. λ: Inflation. Peaks: Associations. Threshold: 5e-8. Colors: Chromosomes.

📈 Manhattan📈 QQ📈 λ📈 Peaks

# Manhattan & QQ Plots
print("=== Manhattan Plot ===")
print("""
Manhattan:
  - X: chromosome
  - Y: -log10(p)
  - Points: SNPs
  - Colors: alternating
  - Threshold: 5e-8

Example:
  Peak at chr6
  → HLA region
  → Association
""")

print("\n=== QQ Plot ===")
print("""
QQ:
  - X: expected -log10(p)
  - Y: observed -log10(p)
  - Diagonal: null
  - Deviation: signal

Example:
  Points on diagonal
  → Well-calibrated
""")

print("\n=== Inflation Factor ===")
print("""
λ:
  - Genomic inflation
  - λ = median(χ²) / 0.456
  - λ = 1: no inflation
  - λ > 1: inflation

Example:
  λ = 1.05
  → Mild inflation
""")

print("\n=== Python Manhattan ===")
print("""
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

def manhattan(df, output="manhattan.png"):
    \"\"\"Manhattan plot.\"\"\"
    df = df.sort_values(['CHR', 'BP'])
    df['ind'] = range(len(df))
    df['logp'] = -np.log10(df['P'])
    
    fig, ax = plt.subplots(figsize=(15, 5))
    
    colors = ['#a855f7', '#6366f1']
    x_labels = []
    x_pos = []
    
    for i, (chrom, group) in enumerate(df.groupby('CHR')):
        ax.scatter(group['ind'], group['logp'],
                   c=colors[i % 2], s=5, alpha=0.7)
        x_labels.append(str(chrom))
        x_pos.append(group['ind'].mean())
    
    ax.axhline(-np.log10(5e-8), color='red', linestyle='--')
    ax.set_xticks(x_pos)
    ax.set_xticklabels(x_labels)
    ax.set_xlabel("Chromosome")
    ax.set_ylabel("-log10(p)")
    ax.set_title("Manhattan Plot")
    
    plt.tight_layout()
    plt.savefig(output)
    plt.show()

# Use
# manhattan(df)
""")

print("\n=== Python QQ ===")
print("""
from scipy import stats

def qq_plot(pvals, output="qq.png"):
    \"\"\"QQ plot.\"\"\"
    n = len(pvals)
    expected = -np.log10(np.arange(1, n+1) / (n+1))
    observed = -np.log10(np.sort(pvals))
    
    plt.figure(figsize=(6, 6))
    plt.scatter(expected, observed, s=5, alpha=0.7, color='purple')
    plt.plot([0, max(expected)], [0, max(expected)],
             'r--', label='Null')
    plt.xlabel("Expected -log10(p)")
    plt.ylabel("Observed -log10(p)")
    plt.title("QQ Plot")
    plt.legend()
    plt.tight_layout()
    plt.savefig(output)
    plt.show()

# Use
# qq_plot(df['P'])
""")

print("\n=== R qqman ===")
print("""
library(qqman)

# Manhattan
manhattan(gwasResults, chr="CHR", bp="BP",
          snp="SNP", p="P", suggestiveline=FALSE,
          genomewideline=-log10(5e-8))

# QQ
qq(gwasResults$P)
""")

print("\n=== Tools ===")
print("""
Tools:
  - qqman (R)
  - ggplot2 (R)
  - matplotlib (Python)
  - LocusZoom
  - FUMA
  - Manhattan plot web tools
""")

print("\n=== Interpretation ===")
print("""
Interpretation:
  - Peaks: associations
  - Height: significance
  - Width: LD
  - λ: inflation

Example:
  Peak at chr6
  → HLA
  → Immune
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - GWAS results
  - Visualization
  - Quality control
  - Publication
  - Communication
""")

🔎 Fine-Mapping & Imputation

🎯 From Association to Causality

Fine-mapping identifies the causal variant(s) within an associated locus. Imputation fills in missing genotypes to increase resolution.

Fine-Mapping

Goal: Causal variant. LD: Correlated SNPs. Methods: Bayesian. Credible set: 95%. Imputation: Fill missing. Tools: FINEMAP, SuSiE, CAVIAR.

🔎 Causal🔎 Credible set🔎 Imputation🔎 FINEMAP

# Fine-Mapping & Imputation
print("=== Fine-Mapping ===")
print("""
Fine-mapping:
  - Identify causal variant
  - Within associated locus
  - LD structure
  - Bayesian methods

Goal:
  - Credible set
  - 95% probability
  - Causal variant
""")

print("\n=== Methods ===")
print("""
1. FINEMAP
   - Bayesian
   - Shotgun stochastic search
   - Fast

2. SuSiE
   - Sum of single effects
   - Bayesian
   - Multiple causal variants

3. CAVIAR
   - Bayesian
   - Credible set
   - Fast

4. PAINTOR
   - Functional annotation
   - Bayesian
   - Integration
""")

print("\n=== Credible Set ===")
print("""
Credible set:
  - 95% probability
  - Contains causal variant
  - Smallest set

Example:
  Credible set: 5 SNPs
  → 95% chance causal is here
""")

print("\n=== Imputation ===")
print("""
Imputation:
  - Fill missing genotypes
  - Reference panel
  - Increase SNPs

Reference panels:
  - 1000 Genomes
  - HRC
  - TOPMed
  - UK Biobank

Tools:
  - IMPUTE2
  - IMPUTE5
  - Beagle
  - Minimac4
  - Michigan Imputation Server
""")

print("\n=== IMPUTE5 ===")
print("""
IMPUTE5:
  - Fast
  - Reference panel
  - Phasing

Command:
  impute5 --haps ref.hap --legend ref.legend --g ref.gen \
          --h target.hap --l target.legend --g target.gen \
          --o output --r chr --m map.txt
""")

print("\n=== Beagle ===")
print("""
Beagle:
  - Phasing
  - Imputation
  - Fast

Command:
  java -jar beagle.jar gt=data.vcf ref=ref.vcf out=imputed
""")

print("\n=== Minimac4 ===")
print("""
Minimac4:
  - Fast
  - Reference panel
  - Michigan Imputation Server

Command:
  minimac4 --refHaps ref.m3vcf --haps target.vcf --prefix output
""")

print("\n=== Quality ===")
print("""
Quality:
  - INFO score
  - > 0.8: good
  - > 0.9: excellent
  - DR2 (mach)
  - R² (beagle)

Example:
  INFO = 0.95
  → High quality
""")

print("\n=== Fine-Mapping Python ===")
print("""
# Use FINEMAP or SuSiE via R
# Python: use subprocess

import subprocess

def run_finemap(z_file, ld_file, n, output="finemap"):
    \"\"\"Run FINEMAP.\"\"\"
    with open(f"{output}.master", "w") as f:
        f.write(f"z;{z_file}\\n")
        f.write(f"ld;{ld_file}\\n")
        f.write(f"n;{n}\\n")
        f.write(f"ss;1\\n")
        f.write(f"config;1\\n")
    
    subprocess.run(["finemap", "--master", f"{output}.master"])
    return output

# Use
# run_finemap("z.txt", "ld.txt", 10000)
""")

print("\n=== Use Cases ===")
print("""
Use cases:
  - Causal variant
  - Functional follow-up
  - Drug targets
  - Mechanism
  - Precision medicine
""")

🛠️ Tools (PLINK, GCTA, BOLT-LMM, GEMMA)

🎯 GWAS Tools

Many tools exist for GWAS analysis. Each has strengths and is suited to different use cases.

Tools

PLINK: QC, association. GCTA: Heritability. BOLT-LMM: Large-scale. GEMMA: Mixed models. SAIGE: Binary. REGENIE: Whole-genome.

🛠️ PLINK🛠️ GCTA🛠️ BOLT-LMM🛠️ GEMMA

# Tools
print("=== PLINK ===")
print("""
PLINK:
  - QC
  - Association
  - Standard
  - Free

Commands:
  plink --bfile data --maf 0.01 --hwe 1e-6 --geno 0.05 --make-bed --out clean
  plink --bfile clean --linear --pheno pheno.txt --covar covar.txt --out assoc
  plink --bfile clean --logistic --pheno pheno.txt --covar covar.txt --out assoc
""")

print("\n=== GCTA ===")
print("""
GCTA:
  - Heritability
  - Mixed model
  - Fast

Commands:
  gcta --bfile data --make-grm --out grm
  gcta --grm grm --pheno pheno.txt --reml --out h2
  gcta --grm grm --mlma --bfile data --out assoc
""")

print("\n=== BOLT-LMM ===")
print("""
BOLT-LMM:
  - Large-scale
  - Fast
  - UK Biobank

Command:
  bolt --bfile=data --phenoFile=pheno.txt --lmm --LDscoresFile=LD.txt
""")

print("\n=== GEMMA ===")
print("""
GEMMA:
  - Mixed model
  - Multiple phenotypes

Commands:
  gemma -bfile data -gk 1 -o kinship
  gemma -bfile data -k kinship.cXX.txt -lmm 1 -o assoc
""")

print("\n=== SAIGE ===")
print("""
SAIGE:
  - Binary traits
  - Related individuals
  - Scalable

Command:
  saige --bfile=data --phenoFile=pheno.txt --phenoCol=disease
""")

print("\n=== REGENIE ===")
print("""
REGENIE:
  - Whole-genome regression
  - Fast
  - Large-scale

Commands:
  regenie --step 1 --bfile data --phenoFile pheno.txt
  regenie --step 2 --bfile data --phenoFile pheno.txt --pred pred.list
""")

print("\n=== Other Tools ===")
print("""
1. PLINK2
   - Faster
   - More features

2. METAL
   - Meta-analysis

3. MR-Base
   - Mendelian randomization

4. FUMA
   - Functional annotation

5. LocusZoom
   - Visualization

6. PRSice
   - Polygenic scores

7. LDSC
   - LD score regression

8. Hail
   - Cloud-scale
""")

print("\n=== Tool Comparison ===")
print(f"{'Tool':<20} {'Type':<20} {'Speed':<15} {'Best For':<20}")
print("-" * 75)
print(f"{'PLINK':<20} {'QC, assoc':<20} {'Fast':<15} {'General':<20}")
print(f"{'GCTA':<20} {'Mixed model':<20} {'Fast':<15} {'Heritability':<20}")
print(f"{'BOLT-LMM':<20} {'Mixed model':<20} {'Very fast':<15} {'Biobank':<20}")
print(f"{'GEMMA':<20} {'Mixed model':<20} {'Fast':<15} {'Multiple':<20}")
print(f"{'SAIGE':<20} {'Binary':<20} {'Fast':<15} {'Related':<20}")
print(f"{'REGENIE':<20} {'Whole-genome':<20} {'Fast':<15} {'Large-scale':<20}")

print("\n=== When to Use Which ===")
print("""
USE PLINK:
  ✓ QC
  ✓ Basic association
  ✓ General

USE GCTA:
  ✓ Heritability
  ✓ Mixed model
  ✓ Relatedness

USE BOLT-LMM:
  ✓ Large-scale
  ✓ Biobank
  ✓ Fast

USE GEMMA:
  ✓ Multiple phenotypes
  ✓ Mixed model
  ✓ Bayesian

USE SAIGE:
  ✓ Binary traits
  ✓ Related individuals
  ✓ Scalable

USE REGENIE:
  ✓ Whole-genome
  ✓ Large-scale
  ✓ Fast
""")

🐍 Python Integration

🎯 GWAS with Python

Python is a powerful language for GWAS analysis, visualization, and automation. Here's how.

Python

Pandas: Data. NumPy: Arrays. Statsmodels: Regression. Matplotlib: Plots. Scikit-learn: PCA. Subprocess: Tools.

🐍 Pandas🐍 Statsmodels🐍 Matplotlib🐍 Automate

# Python Integration
print("=== 1. Load GWAS Data ===")
print("""
import pandas as pd

# Load
df = pd.read_csv("gwas_results.txt", sep="\\t")
print(df.head())
print(df.columns)
""")

print("\n=== 2. Association Testing ===")
print("""
import statsmodels.api as sm
import numpy as np

def association(genotype, phenotype, covariates=None):
    \"\"\"Association test.\"\"\"
    X = genotype.reshape(-1, 1)
    if covariates is not None:
        X = np.hstack([X, covariates])
    X = sm.add_constant(X)
    
    model = sm.OLS(phenotype, X).fit()
    return model.params[1], model.pvalues[1]

# Example
# beta, pval = association(genotype, phenotype)
""")

print("\n=== 3. PCA ===")
print("""
from sklearn.decomposition import PCA

def compute_pca(genotypes, n_components=10):
    \"\"\"PCA.\"\"\"
    pca = PCA(n_components=n_components)
    pcs = pca.fit_transform(genotypes)
    return pcs, pca.explained_variance_ratio_

# Use
# pcs, var = compute_pca(genotypes)
""")

print("\n=== 4. Manhattan Plot ===")
print("""
import matplotlib.pyplot as plt
import numpy as np

def manhattan(df, output="manhattan.png"):
    \"\"\"Manhattan plot.\"\"\"
    df = df.sort_values(['CHR', 'BP'])
    df['ind'] = range(len(df))
    df['logp'] = -np.log10(df['P'])
    
    fig, ax = plt.subplots(figsize=(15, 5))
    colors = ['#a855f7', '#6366f1']
    
    for i, (chrom, group) in enumerate(df.groupby('CHR')):
        ax.scatter(group['ind'], group['logp'],
                   c=colors[i % 2], s=5, alpha=0.7)
    
    ax.axhline(-np.log10(5e-8), color='red', linestyle='--')
    ax.set_xlabel("Chromosome")
    ax.set_ylabel("-log10(p)")
    ax.set_title("Manhattan Plot")
    plt.tight_layout()
    plt.savefig(output)
    plt.show()

# Use
# manhattan(df)
""")

print("\n=== 5. QQ Plot ===")
print("""
def qq_plot(pvals, output="qq.png"):
    \"\"\"QQ plot.\"\"\"
    n = len(pvals)
    expected = -np.log10(np.arange(1, n+1) / (n+1))
    observed = -np.log10(np.sort(pvals))
    
    plt.figure(figsize=(6, 6))
    plt.scatter(expected, observed, s=5, alpha=0.7, color='purple')
    plt.plot([0, max(expected)], [0, max(expected)], 'r--')
    plt.xlabel("Expected -log10(p)")
    plt.ylabel("Observed -log10(p)")
    plt.title("QQ Plot")
    plt.tight_layout()
    plt.savefig(output)
    plt.show()

# Use
# qq_plot(df['P'])
""")

print("\n=== 6. Run PLINK ===")
print("""
import subprocess

def run_plink(bfile, output, command="--linear"):
    \"\"\"Run PLINK.\"\"\"
    cmd = ["plink", "--bfile", bfile, command,
           "--out", output]
    subprocess.run(cmd, check=True)
    return f"{output}.assoc.linear"

# Use
# run_plink("data", "assoc", "--linear")
""")

print("\n=== 7. Parse PLINK Output ===")
print("""
def parse_plink(filepath):
    \"\"\"Parse PLINK association output.\"\"\"
    df = pd.read_csv(filepath, sep="\\s+")
    return df

# Use
# df = parse_plink("assoc.assoc.linear")
""")

print("\n=== 8. Heritability ===")
print("""
import numpy as np

def estimate_heritability(genotypes, phenotype):
    \"\"\"Estimate SNP heritability.\"\"\"
    # GRM
    n = genotypes.shape[0]
    p = genotypes.mean(axis=0) / 2
    Z = genotypes - 2 * p
    K = Z @ Z.T / genotypes.shape[1]
    
    # REML (simplified)
    # ...
    return None

# Use
# h2 = estimate_heritability(genotypes, phenotype)
""")

print("\n=== 9. Polygenic Score ===")
print("""
def compute_prs(genotypes, betas):
    \"\"\"Compute polygenic score.\"\"\"
    return genotypes @ betas

# Use
# prs = compute_prs(genotypes, betas)
""")

print("\n=== 10. Complete Pipeline ===")
print("""
import pandas as pd
import numpy as np
import subprocess
import matplotlib.pyplot as plt

def gwas_pipeline(bfile, pheno, covar, output="gwas"):
    \"\"\"Complete GWAS pipeline.\"\"\"
    # QC
    subprocess.run([
        "plink", "--bfile", bfile,
        "--maf", "0.01", "--hwe", "1e-6",
        "--geno", "0.05", "--make-bed",
        "--out", f"{output}_clean"
    ], check=True)
    
    # Association
    subprocess.run([
        "plink", "--bfile", f"{output}_clean",
        "--linear", "--pheno", pheno,
        "--covar", covar,
        "--out", output
    ], check=True)
    
    # Parse
    df = pd.read_csv(f"{output}.assoc.linear", sep="\\s+")
    
    # Plots
    # manhattan(df)
    # qq_plot(df['P'])
    
    return df

# Use
# df = gwas_pipeline("data", "pheno.txt", "covar.txt")
""")

⚖️ Tool Comparison

🎯 Which Tool?

Choosing the right GWAS tool depends on your data size, trait type, and computational resources.

Comparison

PLINK: Standard. GCTA: Heritability. BOLT-LMM: Biobank. GEMMA: Multiple. SAIGE: Binary. REGENIE: Whole-genome.

⚖️ PLINK⚖️ GCTA⚖️ BOLT-LMM⚖️ GEMMA

Tool	Type	Speed	Trait	Best For
PLINK	QC, assoc	Fast	Both	General
GCTA	Mixed model	Fast	Both	Heritability
BOLT-LMM	Mixed model	Very fast	Quantitative	Biobank
GEMMA	Mixed model	Fast	Both	Multiple
SAIGE	Mixed model	Fast	Binary	Related
REGENIE	Whole-genome	Fast	Both	Large-scale
PLINK2	QC, assoc	Very fast	Both	Modern
Hail	Cloud	Scalable	Both	Cloud

# Decision Guide
print("=== Choose Tool by Data Size ===")
print("""
Small (< 10k):
  → PLINK
  → GEMMA

Medium (10k-100k):
  → PLINK
  → GCTA
  → GEMMA

Large (100k-500k):
  → BOLT-LMM
  → SAIGE
  → REGENIE

Very large (> 500k):
  → BOLT-LMM
  → REGENIE
  → Hail
""")

print("\n=== Choose Tool by Trait ===")
print("""
Quantitative:
  → BOLT-LMM
  → GCTA
  → GEMMA

Binary:
  → SAIGE
  → PLINK
  → REGENIE

Both:
  → PLINK
  → GEMMA
  → REGENIE
""")

print("\n=== Speed Comparison ===")
print(f"{'Tool':<20} {'100k':<15} {'500k':<15} {'1M':<15}")
print("-" * 65)
print(f"{'PLINK':<20} {'1 hour':<15} {'5 hours':<15} {'10 hours':<15}")
print(f"{'BOLT-LMM':<20} {'10 min':<15} {'1 hour':<15} {'2 hours':<15}")
print(f"{'SAIGE':<20} {'30 min':<15} {'2 hours':<15} {'5 hours':<15}")
print(f"{'REGENIE':<20} {'20 min':<15} {'1 hour':<15} {'3 hours':<15}")

print("\n=== When to Use Which ===")
print("""
USE PLINK:
  ✓ QC
  ✓ Basic association
  ✓ Standard

USE GCTA:
  ✓ Heritability
  ✓ Relatedness
  ✓ Mixed model

USE BOLT-LMM:
  ✓ Biobank
  ✓ Large-scale
  ✓ Fast

USE GEMMA:
  ✓ Multiple phenotypes
  ✓ Bayesian
  ✓ Mixed model

USE SAIGE:
  ✓ Binary traits
  ✓ Related individuals
  ✓ Scalable

USE REGENIE:
  ✓ Whole-genome
  ✓ Large-scale
  ✓ Fast
""")

❓ FAQ

🎯 Frequently Asked Questions

Answers to common questions about GWAS and population genetics.

What is GWAS?

What is a SNP?

A SNP (Single Nucleotide Polymorphism) is a variation at a single position in DNA where different individuals have different nucleotides (e.g., A, T, C, or G). SNPs are the most common genetic variants and are the primary markers used in GWAS.

What is population structure and why does it matter in GWAS?

Population structure refers to systematic differences in allele frequencies between subpopulations. It matters in GWAS because it can cause spurious associations (false positives) if cases and controls have different ancestry. Methods like PCA, ADMIXTURE, and linear mixed models correct for structure.

What is linkage disequilibrium (LD)?

Linkage disequilibrium (LD) is the non-random association of alleles at different loci. High LD means alleles are inherited together more often than expected by chance. LD is used to identify haplotype blocks and to perform imputation and fine-mapping in GWAS.

Which tools are used for GWAS?

Common GWAS tools include PLINK (association testing, QC), GCTA (mixed models, heritability), BOLT-LMM (large-scale LMM), GEMMA (mixed models), SAIGE (binary traits, related individuals), and REGENIE (whole-genome regression). Visualization is done with QQ plots and Manhattan plots.

What is the genome-wide significance threshold?

The standard genome-wide significance threshold is p < 5 × 10⁻⁸. This is based on Bonferroni correction for ~1 million independent tests (0.05 / 1,000,000). It is used to control for multiple testing across the genome.

What is a Manhattan plot?

A Manhattan plot displays GWAS results with chromosomes on the x-axis and -log10(p-value) on the y-axis. Each point is a SNP. Significant associations appear as peaks above the genome-wide significance line.

What is a QQ plot?

A QQ plot compares observed p-values to expected p-values under the null hypothesis. Points on the diagonal indicate good calibration. Deviation at the top indicates true associations. The inflation factor λ measures overall deviation.

What is fine-mapping?

Fine-mapping identifies the causal variant(s) within an associated locus. Because of LD, many SNPs may be associated. Fine-mapping uses Bayesian methods (FINEMAP, SuSiE) to define a credible set of variants that likely contains the causal variant.

What is imputation?

Imputation fills in missing genotypes using a reference panel (e.g., 1000 Genomes, HRC, TOPMed). It increases the number of SNPs tested in GWAS and improves fine-mapping resolution. Tools include IMPUTE5, Beagle, and Minimac4.

# Quick Reference
print("=== Quick Answers ===")
print("""
Q: What is GWAS?
A: Genome-wide association study.

Q: What is a SNP?
A: Single nucleotide polymorphism.

Q: Significance threshold?
A: p < 5e-8.

Q: What is LD?
A: Linkage disequilibrium.

Q: What is HWE?
A: Hardy-Weinberg equilibrium.

Q: Population structure?
A: Ancestry differences; correct with PCA/LMM.

Q: Tools?
A: PLINK, GCTA, BOLT-LMM, GEMMA, SAIGE, REGENIE.

Q: Manhattan plot?
A: GWAS visualization.

Q: QQ plot?
A: P-value calibration.

Q: Fine-mapping?
A: Identify causal variant.

Q: Imputation?
A: Fill missing genotypes.

Q: Free?
A: Yes — all major tools are free.
""")

🚀 Future

🎯 Where GWAS Is Going

The future is diverse populations, multi-omics, AI, rare variants, single-cell, and clinical translation.

Future Directions

Diversity: Global. Multi-omics: Integrated. AI: Prediction. Rare: Sequencing. Single-cell: Resolution. Clinical: Translation.

🚀 Diversity🚀 Multi-omics🚀 AI🚀 Clinical

# Future of GWAS
print("=== 1. Diverse Populations ===")
print("""
Trend: Global diversity

Current:
  - Mostly European
  - ~80% European

Future:
  - Global
  - Multi-ancestry
  - Equity

Examples:
  - PAGE
  - H3Africa
  - GBMI

Future:
  - Diverse
  - Equitable
  - Generalizable
""")

print("\n=== 2. Multi-Omics ===")
print("""
Trend: Multi-omics

Current:
  - Genomics only

Future:
  - Genomics + transcriptomics
  - Genomics + proteomics
  - Genomics + metabolomics
  - Genomics + epigenomics

Examples:
  - GTEx
  - UK Biobank
  - TOPMed

Future:
  - Integrated
  - Mechanistic
  - Systems
""")

print("\n=== 3. AI ===")
print("""
Trend: AI + GWAS

Ideas:
  - Deep learning
  - Polygenic scores
  - Fine-mapping
  - Prediction

Examples:
  - DeepWAS
  - Graph neural networks
  - Transformer

Future:
  - Better prediction
  - Better fine-mapping
  - Better understanding
""")

print("\n=== 4. Rare Variants ===")
print("""
Trend: Rare variants

Current:
  - Common variants
  - Arrays

Future:
  - Rare variants
  - Whole-genome sequencing
  - Gene-based tests

Examples:
  - UK Biobank WGS
  - All of Us
  - gnomAD

Future:
  - Rare variant associations
  - Missing heritability
  - Clinical
""")

print("\n=== 5. Single-Cell ===")
print("""
Trend: Single-cell

Current:
  - Bulk

Future:
  - Single-cell
  - Cell-type specific
  - eQTL

Examples:
  - scRNA-seq
  - scATAC-seq
  - Cell atlas

Future:
  - Cell-type resolution
  - Mechanisms
  - Precision
""")

print("\n=== 6. Clinical Translation ===")
print("""
Trend: Clinical

Current:
  - Research

Future:
  - Clinical
  - Polygenic scores
  - Pharmacogenomics
  - Screening

Examples:
  - Breast cancer
  - Cardiovascular
  - Pharmacogenomics

Future:
  - Clinical implementation
  - Precision medicine
  - Equity
""")

# TIMELINE
print("\n=== Timeline ===")
print("""
Past:
  2005: First GWAS
  2007: WTCCC
  2010: Thousands
  2015: Biobanks
  2020: Millions
  2025: Diverse populations

Present:
  2025: Multi-omics
  2026: AI

Future:
  2030: Global
  2035: Clinical
  2040: Precision?
""")

print("\n=== Final Thoughts ===")
print("""
GWAS is:
  - Transforming genetics
  - Finding variants
  - Understanding biology
  - Evolving

The future is:
  - Diverse populations
  - Multi-omics
  - AI
  - Rare variants
  - Single-cell
  - Clinical translation

"GWAS is the key to complex genetics."

Keep exploring. Keep building.
""")